Optical fibers are being developed today for usage in the communications industry. One type of such optical fiber is that termed stepped index which comprises an elongated, transparent core of uniform index of refraction which is encased within a surrounding transparent cladding of a lower refractive index. For communication purposes a series of light pulses are transmitted through the core; however the various light rays of a pulse follow different paths within the core as they reflect back and forth along the boundary of core and cladding. As a consequence the pulse length elongates during core travel which in turn restricts fiber bandwidth.
In order to increase bandwidth and thereby provide a multimode, high-capacity optical fiber communications system another type of optical fiber has been developed which is termed graded index. With this type of optical fiber the fiber core has an index of refraction that varies radially from the core axis to the core periphery. Ideally, the distribution of refractive indices within the core should be such as to cause all light rays of a pulse to travel along the fiber at the same axial velocity regardless of traversed path length variations. In actuality, of course, there will be some deviation from optimum refractive index distribution of the core made during fiber manufacture. The manufacturer must therefore monitor this distribution to insure that various variations remain within specified tolerances.
Heretofore, the most accurate method of monitoring such index of refraction distribution profiles has been that of the slab method. This involves a rather elaborate, tedious and time consuming preparation of a fiber sample whereby a thin slide is cut out from the fiber and polished to a high degree of flatness and parallelism of opposed surfaces. The samples, which are then examined with an interference microscope, act as phase objects that displace in the core region the normally straight parallel fringe lines of the microscope output field. The fringe displacements or shifts are proportional to differences in the indices of refraction within the various radial regions of the core and that of the cladding.
Recently, non-destructive approaches have been taken in determining index distribution profiles. These are disclosed in the article by Hunter and Schreiber titled "Mach-Zehnder Interferometer Data Reduction Method for Refractively Inhomogeneous Test Objects", Applied Optics, Vol. 14, No. 3, (March, 1975), in the article by Marhic, Ho and Epstein titled "Nondestructive Refractive-Index Profile Measurement of Clad Optical Fibers", Applied Physics Letters 26 (1975), and also in the article by Kokubun and Iga titled "Precise Measurement of the Refractive Index Profile of Optical Fibers by a Nondestructive Interference Method", Transactions of the IECE of Japan, Vol. E60, No. 12 (December, 1977). A common aspect of these methods is that a beam of light is passed transversely through the optical fiber and into a Mach-Zehnder interferometer. Hunter and Schreiber originally concluded that fringe shift contributions due to the refractive medium could not be reduced with an inverted Abel integral equation to determine accurately the internal index of refraction distribution that was thought to be possible since the refraction angles of probing rays would be known. Kokubun and Iga however found a mathematical error in the integral equation used by Hunter and Schreiber and in turn concluded that a correct algorithm had indeed been found for non-destructive index determination with transverse illumination.
Notwithstanding the clarification provided by Kokubun and Iga, the solution of the integral equation remains accomplishable only by an extremely complex method of successive approximation involving a Taylor series expansion. The change in index of refraction of the core is thus considered as being in a series of discrete steps as a function of core radius. The index of refraction at any one ring, N.sub.r, may be stated as N.sub.r =N.sub.o -.DELTA.N(r/a).sup..alpha. where r designates radial position, as is the outside radius of the outermost ring, N.sub.o is the refractive index at core center where r=o, .DELTA.N is the difference in refractive index between core center and cladding where r=o and .alpha. is a dimensionless number that characterizes the shape of the core index profile.
In addition to the just described complexity of the prior art approaches for determining index profile, they also have been based on the assumption that the core is circular and, in general, that .alpha. remains uniform throughout the core, which it often does not. For example, some optical fibers have a barrier layer at the interface of core and cladding which causes the index at this position actually to be less than that of the cladding. In such a situation the above equation becomes completely invalid as a model. Furthermore, results of the successive approximation method have not been shown in actual comparisons with slab measurements on the same fibers.
Recently, in a 1977 article by Saunders and Gardner which appeared in Vol. 16 of Applied Optics titled "Nondestructive Interferometric Measurement of the Delta and Alpha of Clad Optical Fibers" another, similar method is discussed. The analysis here however is restricted to power law profiles characterized by two constants, namely the refractive index difference between the maximum value at core center and the cladding value, and the power law coefficient which is the same profile shape characterization .alpha.. Therefore this analysis also assumes a circular core and a uniform .alpha. throughout the core fiber.
Accordingly, it is a general object of the present invention to provide an improved method of determining an index of refraction profile of an optical fiber.
More specifically, it is an object of the invention to provide an improved, non-destructive type method of determining an optical fiber index of refraction profile of the type wherein an interferogram is formed with light passed transversely through the fiber.
Another object of the invention is to provide a method of determining an index of refraction profile of the type described which does not require assumption of any particular functional shape of index distribution.